PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of JET D....

PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of

JET

D. Tskhakaya1,*, A. Loarte2, S. Kuhn1, and W. Fundamenski3

1Plasma and Energy Physics Group, Association Euratom – ÖAW, Department

of Theoretical Physics, University of Innsbruck, Innsbruck, Austria2EFDA, Close Support Unit Garching, Max-Planck-Institut fuer Plasmaphysik,

D-85748 Garching bei Muenchen, Germany3UKAEA Fusion, Association Euratom-UKAEA, Culham Science Center,

Abingdon, United Kingdom

*Permanent address: Institute of Physics, Georgian Academy of Sciences,

Tbilisi, Georgia

Outline of the Talk

• Introduction

• Characteristics of the codes EDGE2D-NIMBUS and BIT1

• Results of test simulations

• Results of ELM-free and ELMy SOL simulations

• Conclusions

D. Tskhakaya et. al., 9th EU-US Transport Task Force Workshop Córdoba, Spain, (2002)

Introduction • Investigation of the energy and particle transport inside the SOL

during ELM activity is an extremely important topic, especially for predicting the heat loads on the divertor plates of next-generation fusion devices [Loarte et al., 2000, 2001].

• The short time scale of the process and the low collisionality of the ELM-produced highly energetic particles define the kinetic nature of ELMy transport.

• Despite its importance, kinetic simulations of the ELMy SOL are rare. Simulations done up to now use either simplified linear profiles for neutrals [Tskhakaya, et al., 2001], or do not consider them at all [Bergmann, 2002]. Hence, they correspond to very simplified SOL models with low recycling.

2 D Modelling of the Plasma Edge of Fusion Devices (EDGE2D, B2-Eirene)

• The plasma edge is modelled with 2-D Fluid (plasma) + 2-D Monte Carlo Codes (neutrals)

2-D Fluid equations

A : Density, Momentum and Energy (e-, D+, Z+).

Particle, momentum, energy of the neutrals computed with Monte Carlo Codes (Nimbus, Eirene)

Fluid + Monte Carlo are iterated to convergence

inksources SSAt

A

||

Advantages of 2-D Modelling of EDGE Plasmas • Realistic 2-D geometry • Fully time-dependent & consistent plasma solution with sources and sinks

Disadvantages of 2-D Modelling of EDGE Plasmas • Fluid approximation is not fulfilled in many interesting edge plasma conditions (ELMs, hot ions in SOL, etc.)

ELMs are modelled by increasing ELM, DELM ~ (10 - 1000) x 0, D0 during ELM in pedestal & SOL Experiments p@ELM ~ (1 - 2) p@between ELMs

ELM simulation for ITER with B2-Eirene [Loarte, 2000]

Pedestal only Pedestal + SOL

Te Te @ ELM

Radiation Radiation @ EL

PIC code BIT1 The 1d3v (one space and three velocity dimensions) code BIT1 was developed on the basis of the XPDP1 code from Berkeley. During the simulation the motion of a large number (up to some 106)

of ions and electrons is followed:

.)0,0,(

N, , 2, 1, i ,

,

x

ii

ii

ii

EE

VXdt

d

BVEm

qV

dt

d

Nonlinear Coulomb and charged-neutral particle collisions

.,0

2 xxx E

Coulomb collisions and charged-neutral particle collisions are modelled via a binary collision model, so that the total momentum and the energy is conserved during a collision :

Choosing random pairs Colliding particles

At present the code does not follow neutrals, and assumes fixed neutral density and temperature profiles. All (relevant to the SOL) charged-neutral particle collisions between hydrogen isotopes are implemented:

Elastic A + e - A + e Excitation A + e - A* + e Ionization A + e - A+ + 2e

Elastic A + A+ - A + A+

Charge-exchange A + A+ - A+ + A A = H, D, T

Charged-neutral particle collision cross-sections

10-3

10-1

101

10310

-1

100

101

E [eV]

10-18 m2

elasticcharge exchange

100

102

10410

-2

10-1

100

101

102

E [eV]

10-20 m2

ionizationelastic collisionexcitation

Secondary electron emission is implemented in the code.

Secondary electron emission due to electron impact

./108.1,0

,/108.1,18.010/5

56

smVif

smVifsmVi

i

2,60,cos/1,/22exp 00

0 elseifEEE

Ee

For graphite ,3000 eVE

Secondary electron emission due to ion impact [Diem, 2001]

.10

0 1000 20000

0.2

0.4

0.6

0.8

1

E [eV]

e

0 400 8000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

V [km/s]

i

Particle sourceDivertor

plate

Divertor plate

x

B

Simulation geometry

During the simulation, the Maxwell-distributed electrons and ions are injected into the source region. Particles reaching the divertor plates are absorbed. In the PIC simulation neutral density and temperature profiles are used from the corresponding fluid simulations.

Fluid simulation

Neutral density and temperature

PIC simulation

Test simulations

0 1 2 3 4 5 6 7-4

-3

-2

-1

0

1

2

3

4x 10

5

qx [W/m2]

x [m]

PICSpitzer (Sp.)Sp.+sheath

Source effect

Electron heat flux profile from PIC, and corresponding Spitzer-Härm and the Spitzer-Härm + “sheath” heat fluxes. e=130.

• Sheath effects play an important role not only in the ELMy but also in the ELM-free SOL

ELM-free and ELMy SOL simulations

Mismatch between fluid and kinetic (PIC) simulations

It is necessary to shorten the simulated SOL (scaling has to be conserved).

During the PIC simulation the plasma density and temperature at the source cannot be controlled directly. Input parameters are the particle source intensity and the temperature of injected particles.

Source effect: There are peaks in the density and the temperature profile.

• the absence of sheath in the fluid simulation results in a higher plasma density at the wall than in the PIC simulation. Hence, in order to have a similar charged- neutral collisionality in the PIC simulation it is necessary

to shift the neutral density (obtained from the fluid model).

0 5 10 150

2

4

6

8

10

12x 10

18

x [mm]

nN

(fluid)

ni (fluid)

ni (PIC)

nN

(PIC)

Two sets of simulations have been made for low and high recycling SOL

0 2 4 6 80

0.5

1

1.5

2

2.5

3x 1019

n [m-3]

x [m]

FluidPIC

0 2 4 6 80

50

100

150

200

250T [eV]

x [m]

Ti Fluid

Te Fluid

Ti PIC

Te PIC

Low recycling ELM-free SOL

0 2 4 6 80

5

10

15 x 1019

n [m-3]

x [m]

FluidPIC

0 2 4 6 80

50

100

150

200T [eV]

x [m]

Ti Fluid

Te Fluid

Ti PIC

Te PIC

High recycling ELM-free SOL

ELMy SOL for JET-like conditions

• PeEDGE = 2.5 MW, Pi

EDGE = 6.5 MW

nsepbefore ELM = 0.8 1019 m-3 (low recycling)

= 1.7 1019 m-3 (high recycling) e,i before ELM = 0.75 m2/s, D before ELMe = 0.10 m2/s

• nsepELM = 5 1019 m-3 (low recycling)

= 1020 m-3 (high recycling) Te,i

ELM = 1.5 keV (low recycling) = 0.75 keV (high recycling)

ELM/before ELM = DELM/D before ELM = 100

ELM = 200 s , WELM ~ 100 kJ

Low recycling case

The secondary electrons (SE) do not play any significant role

Potentil and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.

0 2 4 6 80

500

1000

1500

2000Potential [V]

x [m]

without SE (t=0 mks)with SE (t=0 mks)without SE (t=150 mks)with SE (t=150 mks)

0 2 4 6 80

200

400

600

800

1000

Te [eV]

x [m]


0 2 4 6 80

1

2

3

4

5x 1019

ne [m-3]

x [m]

t=0 mkst=50 mkst=200 mkst=250 mkst=400 mks

0 2 4 6 80

500

1000

1500

2000

2500Potential [V]

x [m]


0 2 4 6 80

200

400

600

800

1000

1200

1400

Ti [eV]

x [m]


0 2 4 6 80

200

400

600

800

1000T

e [eV]

x [m]


0 100 200 300 4000

0.5

1

1.5From fluid simulation

t [mks]

n [x2.1019 m-3]T

e [keV]

Ti [keV]

0 50 100 150 2000

500

1000

1500

2000

2500Potential [V]

t [mks]

0 2 4 6 8-4

-2

0

2

4x 105

V||i

[m/s]

x [m]


0 50 100 150 2000

2

4

6

8

10 x 1023

F [1/sm2]

t [mks]

Fe (outer divertor)

Fi (outer divertor)

Fe (inner divertor)

Fi (inner divertor)

From PIC simulation

From PIC simulation

From PIC simulation

0 100 200 300 4000

100

200

300

400

500From fluid simulation

t [mks]

q MW/m2

From PIC simulation

0 100 2000

100

200

300

400

500q

x [MW/m2]

t [mks]

El. (outer divertor)Ions (outer divertor)El. (inner divertor)Ions (inner divertor)

High recycling case

The secondary electrons (SE) do not play any significant role

0 2 4 6 8-300

-200

-100

0

100

200

300

400

500Potential [eV]

x [m]


Potential and electron temperature profiles in the SOL, as parameters most „sensitive“ to the SE.

0 2 4 6 80

50

100

150

200

250

300

350

Te [eV]

x [m]


0 2 4 6 80

0.5

1

1.5

2x 1021

ne [m-3]

x [m]

t=0 mkst=65 mkst=130 mks

0 2 4 6 8-200

0

200

400

600

800Potential [V]

x [m]


0 2 4 6 80

50

100

150

200

250

300

350

Te [eV]

x [m]


0 2 4 6 80

200

400

600

800

1000T

i [eV]

x [m]


0 2 4 6 8-1

0

1

2

3

4

5x 106

V||e

[m/s]

x [m]


0 2 4 6 8-3

-2

-1

0

1

2

3x 105

V||i

[m/s]

x [m]


0 1000 200 300 4000

200

400

600

800

1000


t [mks]

n [x1017 m-3]T

e [eV]

Ti [eV]

0 100 200 300 4000

200

400

600

800


t [mks]

q MW/m2

From PIC simulation From PIC simulation

• Sheath effects play an extremely important role in both

the ELM-free and the ELMy SOL:

i. The electron heat flux due to the “cut-off” effect can exceed the

Spitzer-Härm heat flux even in a highly collisional regime.

ii. the potential drop in the sheath affects the time scale of heat loads

on the divertor plates during the ELM.

• The secondary electrons do not play any significant role

in the ELMy SOL

Conclusions

• During ELM activity the time evolution of the heat load

on the divertor plates exhibits two peaks:

i. The first (small) one appears in an electron time scale after ELM

set-on and corresponds to highly energetic ELM electrons arriving

at the divertor.

ii. The second peak corresponds to the main ELM burst propagating

through the SOL with a high-energy ion speed.

• For more realistic modelling of the ELMy SOL it is

necessary to consider the neutrals self-consistently

Conclusions

PIC simulations of the propagation of type-1 ELM-produced energetic particles on the SOL of JET D....

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